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Tuesday, March 3, 2015



Smullyan on 'not', 'and', 'or', 'if', 'all', 'some (at least one)', and 'the'.

Bartlett defines Grice as a logician -- So is Smullyan. (He was a student of Carnap -- visit the Carnap Corner).

Raymond Smullyan (known as "Ray" -- "I always found the "-mond" otiose") was brought up in Far Rockaway Peninsula in Queens.

The name "Rockaway" may be misleading: it's Native American, and variant spellings include: Requarkie, Rechouwakie, Rechaweygh, Rechquaakie and 
Reckowacky. Its meaning is unclear or was unclear to the Dutch when they settled 
in the area, and they just kept it for lack of an idea of a better name

One day, his brother told him:

"Today is April Fool's Day, and I will fool you as you have never been 
fooled before."

As Smullyan recalled, he laid in bed long after the lights were  turned out
wondering whether or not I had really been fooled. Smullyan concluded  that
indeed his brother had fooled him "as he'd never been fooled before" -- by 
not fooling him.

This was perhaps the first paradox that Smullyan ever encountered.

When Smullyan was thirteen years old his family moved from the Peninsula to

Smullyan attended the Theodore Roosevelt School in the Bronx.

However, Smullyan wanted to learn about groups, rings and fields, the 
foundations of mathematics and mathematical logic.

This the Theodore Roosevelt School did not offer, so Smullyan  left the
school for good to study on his own.

A few years of study certainly put him in a good position to sit the 
College Board examinations, which he did and entered "The Pacific", not the 
ocean, but a college in Oregon.

Soon Smullyan moved to Reed, in Oregon (named after E. Abingdon, Mass.-born
Simeon Gannett Reed and his spouse Amanda, née Wood.  -- Reed's estate was
left to his spouse, with instructions to use it to assist in the cultural
and  intellectual development of Portland. When Mrs. Reed died not much
progress  towards the instructions of her spouse. But not long after, the  Reed
estate established Reed in Portland. W. M. Ladd (son of Reed's former 
partner W. S. Ladd) provided the lands on which Reed stands today, and almost 
all of Reed's estate was passed onto Reed).

After Reed, Smullyan went south, to San Francisco, and stayed there,  but
not for long.

He returned to New York ("where I belonged") where he continued to study 
logic on his own.

He played chess a lot. One of his friends said to him, "If *I* were to 
compose a chess problem, it would be to deduce what happened earlier in the 

This struck Smullyan as a fascinating idea, and was his source for his 
studies in "retrograde analysis" -- that looks for a problem which has a unique
solution, yet looks quite impossible.

Later, he enrolled at the University of Wisconsin, moving after two  terms
to Chicago where he began to take courses at the university but gave  up
after only one semester.

He continued to study on his own.

He then returned to New York where he spent two years. During these years 
he performed in nightclubs in Greenwich Village.

He later returned to Chicago, took various courses at the university  while
continuing to perform at nightclubs. His patter was especially hilarious 
(although himself a shy person).

He also worked as a salesman for a vacuum cleaner company.

One of Smullyan's teachers at the University of Chicago was Rudolf Carnap 
('if you've heard of him, or even if you haven't', as Geary quips).

Carnap recommended Smullyan for a mathematics post at Dartmouth, the 
liberal arts college in Hanover, New Hampshire -- named after the earl of 
Dartmouth -- i.e. the earl of the mouth of the river Dart in Devon, England.

Smullyan had no formal qualifications at this time.

Smullyan taught at Dartmouth while he earned his B.S. from the University 
of Chicago.

Smullyan published an essay, "Languages in which self-reference is 
possible" in The Journal of Symbolic Logic. It is about languages in which 
self-reference is possible.

His next essay was "Undecidability and recursive inseparability" which 
aimed to prove two results on undecidability.

By the time the second of these essays appeared, Smullyan was at  Princeton
working under Alonzo Church for his [i.e. Smullyan's, not Church's] 

After being awarded his Ph.D. from Princeton, he was appointed to  a post
there, at Princeton -- named after some prince [There is no official 
documentary backing, but Princeton is considered to be named after Prince  William
of Orange. My favourite theory is that the name came from a large 
land-owner, Mr. Henry Prince, but I grant a royal prince seems a  more 'verifiable'
eponym for the settlement, as three nearby towns had  similar names, to wit:
Kingston, Queenstown and Princessville -- and it is  hard to derive
"Princesville" from Mr. Henry Prince]

Smullan published several mathematical essays ('entertaining if you are 
into that sort of thing', Geary editorialises) during this  Princeton period.

And essay entitled, "Exact separation of recursively enumerable sets within
theories" was written jointly with Hilary Putnam.

Smullyan also published the essay "Theories with effectively inseparable 
nuclei", to be followed by "Extended canonical systems", "Elementary formal 
systems", and "Monadic elementary formal systems" -- "Not precisely items of
the  New York Times bestselling list", Geary comments).  

Smullyan also published the essay, "Theory of formal systems"  which was
published by Princeton University Press.

Kreisel (whom Witters loved) reviewed the book, and says that it gives a 
"most elegant exposition of the theory of recursively enumerable sets -- a 
striking improvement over previous expositions."

Smullyan was later appointed to the Yeshiva in New York, and then moved to 
Lehman (formerly Hunter's Bronx campus, which at the time joined the City 
University of New York).

Later he went to Indiana, and took the Oscar Ewing chair (named after 
Greensburg-born O. R. Ewing)

Smullyan's publications include essays on the foundations of mathematics 
and mathematical logic.

Usually Smullyan begins with fun-filled monkey tricks and brain-teasers 
with devilish new twists, spinning a logical labyrinth of even more complex
and  challenging problems as he delves into some of the deepest paradoxes of
logic  and set theory, including Gödel's revolutionary theorem of
undecidability. He  provides a guided tour of Infinity, explaining the pioneering
discoveries of  Georg Cantor, who was the first to put the subject on a logically
sound  basis.

He also published "First-order logic", which deals primarily with the 
proofs of, and the interconnections between, various formulations of the 
completeness theorem for first-order logic. The book combines elegance with 
clear, detailed exposition.

"A good student should be able to read it almost without a teacher."  --
unless you count the author of the book as a teacher, figuratively.

He also published "Gödel's incompleteness theorems", which he wrote  "for
the philosopher or any other curious reader who has at least a nodding 
acquaintance with the symbolism of first-order logic, and who can recognize the 
logical validity of a few elementary formulas."

The essay on incompleteness theorems was the first of a series of texts 
which appeared in quick succession.

It was followed by "Recursion theory for metamathematics" and 
"Diagonalization and self-reference" ('the first part deals with  diagonalisation; the
second with self-reference', Geary's review reads).

Smullyan co-authored with Melvin Fitting "Set theory and the continuum 
problem" where consistency and independence proofs are given along with some 
charming set pieces on countability and uncountability and on mathematical 

In the classroom, Smullyan is anything but leisurely or quiet.

Those who watched him teach a logic course, would see him lurch  to the
blackboard (where he writes in a serviceable hand and in complete  sentences)
and paced about his desk, fidgeting and chuckling.

He occasionally breaks into a small sibilant laugh at problems that  seemed
to leave his students somewhat confused than amused (as perhaps  Smullyan's
laugh would indicate).

One of Smullyan's hobbies is astronony. He loves observing through his 
telescope, and he ground the six inch mirror himself.

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